An isolation circuit for signal transmission across an isolation barrier may include a coil that is magnetically coupled to a magnetoresistive (MR) element or giant magnetoresistive (GMR) element. The MR or GMR element has a resistance that is variable in response to a magnetic field applied by the coil. The isolation circuit may include a Faraday shield interposed between the coil and the MR element. The entire structure may be formed monolithically as an integrated circuit on a single substrate.